Algebraic reconstruction technique
The algebraic reconstruction technique is an iterative reconstruction technique used in computed tomography. It reconstructs an image from a series of angular projections. Gordon, Bender and Herman first showed its use in image reconstruction; whereas the method is known as Kaczmarz method in numerical linear algebra.
An advantage of ART over other reconstruction methods is that it is relatively easy to incorporate prior knowledge into the reconstruction process.
ART can be considered as an iterative solver of a system of linear equations, where:
Given a real or complex matrix and a real or complex vector, respectively, the method computes an approximation of the solution of the linear systems of equations as in the following formula,
where, is the i-th row of the matrix, is the i-th component of the vector.
is an optional relaxation parameter, of the range. The relaxation parameter is used to slow the convergence of the system. This increases computation time, but can improve the signal-to-noise ratio of the output. In some implementations, the value of is reduced with each successive iteration.
